In the past few years, there have been impressive breakthroughs to enhance the structure of organic solar cells (OSCs) in order to improve the performance. Resulting in increment of the power conversion efficiency (PCE) from 5% to 18% in OSCs and up to 25% in OSCs module. The Developments cause these thin and flexible, eco-friendly, and low-cost photovoltaic devices to be promising technology for wide range of applications such as internet of things (IOT), sensors, architecture, and wearable electronics.In the past few years, there have been impressive breakthroughs to enhance the structure of organic solar cells (OSCs) in order to improve the performance. Resulting in increment of the power conversion efficiency (PCE) from 5% to 18% in OSCs and up to 25% in OSCs module. The Developments cause these thin and flexible, eco-friendly, and low-cost photovoltaic devices to be promising technology for wide range of applications such as internet of things (IOT), sensors, architecture, and wearable electronics. Further, in this article, fundamental characteristics, operation principles, charge carriers transport mechanisms, and electrical model parameters of an OSC is reviewed. Considering polymers as main and most common building blocks of an OSC, charge transport and current models also have been studied. In addition, mobility characteristics, as one of the critical parameters affecting the OSC performance has investigated. Time of flight (TOF), space charge limited current (SCLC), charge extraction by linearly extracting voltage (CELIV), and impedance spectroscopy as the four fundamental methods to measure mobility in OSCs along with discussion about the advantages and drawbacks of each technique have been studied.